The Information-Topological Register Model: Computational Proof of Concept and the Emergence of Macroscopic Gravity

This manuscript presents the computational verification of the Information-Topological Register Model (Phase A). While previous works analytically derived mass-energy equivalence and macroscopic gravity from a discrete 1D topological manifold, this paper provides the algorithmic proof of concept. Using a discrete Markov-chain algorithm applied to an unweighted graph network, we simulate the foundational axiom of topological stress diffusion. Without encoding any classical metric distances, continuous space, or predefined gravitational parameters, the simulation demonstrates that a purely localized transfer of information bits deterministically generates a macroscopic 1/r gravitational potential. Key Findings and Computational Demonstrations: • The 1/r Macroscopic Divergence: The simulation proves that blind, discrete node updates inevitably converge into the macroscopic geometry of curved spacetime, perfectly mirroring the Newtonian gravitational potential and the exact Schwarzschild metric (g₀0 = 1 - S (r) ). • Near-Horizon Quantum Granularity: Close to the theoretical event horizon (dgeo = 2 to 5), the simulation reveals a distinct vertical scattering of topological stress. This visualizes topological quantum fluctuations, proving that space is granular and discrete at the microscopic scale. • Emergence of the Continuum: At macroscopic distances (dgeo > 5), the massive number of microscopic topological connections averages out. The underlying discrete graph network mathematically masquerades as a perfectly smooth, continuous 3D volume, effectively bridging quantum mechanics and General Relativity. Important Contextual Note: This simulation focuses strictly on macroscopic metric generation and the thermodynamic relaxation of the vacuum (Phase A of the Register Model). The microdynamic momentum propagation and quantum non-locality described in Work 4 (The Topological Guidance Equation) govern particle kinematics within this already generated metric and are therefore systematically excluded from this baseline spatial simulation.